Question 964462
y = −3(x−3)^2 +108
y = -3(x^2 -6x +9) +108
y = -3x^2 +18x -27 +108
y = -3x^2 +18x +81
Note This is a parabola that opens downward, therefore we want the coordinates of the vertex,
x = -b/2a = -18 / 2(-3) = 3
now substitute x = 3 in the equation above
y = -3(3^2) +18(3) +81
y = -27 +54 +81
y = 108
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1) hovercraft reaches maximum height in 3 seconds
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2) maximum height is 108 meters
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3) -3x^2 +18x +81 = 0
(-3x-9)(x-9) = 0
-3x = 9
x = -3 and x = 9
we want the positive value for x
The hovercraft will land on the ground in 9 seconds
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4) y = -3x^2 +18x +81
substitute x = 0
y = 81
The hovercraft is at a height of 81 meters at time 0 seconds
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